A new numerical scheme for discrete constrained total variation flows and its convergence

In this paper, we propose a new numerical scheme for a spatially discrete model of total variation flows whose values are constrained to a Riemannian manifold. The difficulty of this problem is that the underlying function space is not convex; hence it is hard to calculate a minimizer of the functional with the manifold constraint even if it exists. We overcome this difficulty by “localization technique” using the exponential map and prove a finite-time error estimate. Finally, we show a few numerical results for the target manifolds$$S^2$$S2andSO(3).